Model Selection: Identifying the Z vars

0.1 Summary

From all the combination of Z variables for a particular outcome I use the following methods for model selection

1. Filter those results for which the sign of the double interaction terms for GQ and NSEW (\(Distance^{GQ/NSEW}_{i, 0-40}*Post^{GQ/NSEW}_{i,t}\)) is positive.
   1. From all the specifications with positive terms, I pick the spec that minimizes the combined p value of all the terms of interest.
   2. The second method picks the specification that maximizes the
2. Maximizes the adjusted R square
   1. Maximize without checking for the signs on the double interaction terms for GQ and NSEW
   2. Filter out those that have positive GQ and NSEW and then maximize R-Square
3. Minimizes the Bayesian information criterion (BIC)
4. Minimizes the Akaike information criterion (AIC).

The current specification for selecting z variables is as follows: \[Y_{i,t} = Distance^{GQ}_{i} + Distance^{NSEW}_{i} + Z^{capital}_{i,t} + Z^{labour}_{i,t} + Z^{land}_{i,t} + Z^{product}_{i,t} + Distance^{GQ}_{i}*Post^{GQ}_{i,t} + Distance^{NSEW}_{i}*Post^{NSEW}_{i,t} + \\Distance^{GQ}_{i}*Post^{GQ}_{i,t}*Z^{capital}_{i,t} + Distance^{GQ}_{i}*Post^{GQ}_{i,t}*Z^{labour}_{i,t} + Distance^{GQ}_{i}*Post^{GQ}_{i,t}*Z^{land}_{i,t} + Distance^{GQ}_{i}*Post^{GQ}_{i,t}*Z^{product}_{i,t} \\+ Distance^{NSEW}_{i}*Post^{NSEW}_{i,t}*Z^{capital}_{i,t} + Distance^{NSEW}_{i}*Post^{NSEW}_{i,t}*Z^{labour}_{i,t} + Distance^{NSEW}_{i}*Post^{NSEW}_{i,t}*Z^{land}_{i,t} +\\ Distance^{NSEW}_{i}*Post^{NSEW}_{i,t}*Z^{product}_{i,t} + State * Year\]

NOTE The outcome log of GDP per capita has no combinations of z variables for which both the NSEW and GQ double interaction terms (\(Distance^{GQ}_{i}*Post^{GQ}_{i,t}\)) are both positive.. The only change in the specification was that the Z variables for land were reduced to only cr_s.

unique(regressionResults$yVar)[!(unique(regressionResults$yVar) %in% unique(pValueSelection$yVar))]

[1] "logGdpPc"

0.2 Making all the charts

The code for creating the results is hidden to make this report concise. The section below loops through all the results for each model selection process and creates charts for each.

All the charts in reference to the terms that are relevant for GQ

1 1. All minimum P Value

varList <- zVars %>% 
        mutate(zVarCombo = paste(capitalVar, labourVar, landVar, productVar, sep = ", ")) %>% 
        select(yVar, zVarCombo)
for(i in 1:length(varList$yVar)){
        yvarTemp <- varList[i, ]$yVar
        zVarComboTemp <- varList[i, ]$zVarCombo
        
        chartData <- percentileValues %>% 
                filter(yVar ==  yvarTemp & zVarCombo == zVarComboTemp)
        
        titleName <- unique(chartData$title)
        subTitleName <- unique(chartData$zVarCombo)
        print(createCharts(chartData, titleName, subTitleName))
}

2 2. GQ/NSEW minimum P Value

varList <- zVars %>% 
        mutate(zVarCombo = paste(capitalVar, labourVar, landVar, productVar, sep = ", ")) %>% 
        select(yVar, zVarCombo)
for(i in 1:length(varList$yVar)){
        yvarTemp <- varList[i, ]$yVar
        zVarComboTemp <- varList[i, ]$zVarCombo
        
        chartData <- percentileValues %>% 
                filter(yVar ==  yvarTemp & zVarCombo == zVarComboTemp)
        
        titleName <- unique(chartData$title)
        subTitleName <- unique(chartData$zVarCombo)
        print(createCharts(chartData, titleName, subTitleName))
}

3 3. Maximizing R-SQUARE

varList <- zVars %>% 
        mutate(zVarCombo = paste(capitalVar, labourVar, landVar, productVar, sep = ", ")) %>% 
        select(yVar, zVarCombo)
for(i in 1:length(varList$yVar)){
        yvarTemp <- varList[i, ]$yVar
        zVarComboTemp <- varList[i, ]$zVarCombo
        
        chartData <- percentileValues %>% 
                filter(yVar ==  yvarTemp & zVarCombo == zVarComboTemp)
        
        titleName <- unique(chartData$title)
        subTitleName <- unique(chartData$zVarCombo)
        print(createCharts(chartData, titleName, subTitleName))
}

4 3. Maximizing R-SQUARE After filtering positive GQ/NSEW

varList <- zVars %>% 
        mutate(zVarCombo = paste(capitalVar, labourVar, landVar, productVar, sep = ", ")) %>% 
        select(yVar, zVarCombo)
for(i in 1:length(varList$yVar)){
        yvarTemp <- varList[i, ]$yVar
        zVarComboTemp <- varList[i, ]$zVarCombo
        
        chartData <- percentileValues %>% 
                filter(yVar ==  yvarTemp & zVarCombo == zVarComboTemp)
        
        titleName <- unique(chartData$title)
        subTitleName <- unique(chartData$zVarCombo)
        print(createCharts(chartData, titleName, subTitleName))
}

4.1 Temporary section for checks

step(plm(logGdpPc ~ gqDistType + nsewDistType + e_pr_fin3 + edu_ter_15_t+ cr_s + est_sh_1 + gqDistType * postGQ + nsewDistType * postNSEW + gqDistType * postGQ * e_pr_fin3 + gqDistType * postGQ * edu_ter_15_t + gqDistType * postGQ * cr_s + gqDistType * postGQ * est_sh_1 + nsewDistType * postNSEW * e_pr_fin3 + nsewDistType * postNSEW * edu_ter_15_t + nsewDistType * postNSEW * cr_s + nsewDistType * postNSEW * est_sh_1 + gqDistType*postGQ*nsewDistType*postNSEW + spatialState * year, data = allData), direction = "both")

This series is NA and has been removed: hous_slm

Error in UseMethod("extractAIC") : 
  no applicable method for 'extractAIC' applied to an object of class "c('plm', 'panelmodel')"
In addition: There were 14 warnings (use warnings() to see them)